I love using molasses in many different recipes, but I have found it difficult to avoid making a mess when using it. Both spooning molasses from the jar and trying to pour it out wind up leaving molasses trails on the jar and my working surface, which if not wiped off immediately dry into a mass that is almost impossible to clean.
Try slowly twisting the jar as you slow down your pour. This is what I do and it works pretty well.
This is actually something you'll see waiters and bartenders do when pouring wine, too. This video shows the action at around 3:20 in.
Twisting the bottle causes the drip to collect on the inside of the rim and keeps it from dripping down the side. Because the molasses is more viscous than wine, it may take a bit more turning but it does work well.
Can you pour your molasses into a squeeze bottle? A lot of beekeeping supply outlets sell caps that work very well with thicker viscous fluids like honey which is very similar to molasses in that regard.
Alternatively. It helps to turn the jar as you stop pouring so that last bit of drizzle gets tossed/twisted into the jar.
Use a flip-top bottle.
Some brands of molasses are sold in flip-top bottles. They make it much easier to dispense the exact amount desired, with less chance of making a mess. You still have to watch the bottle for occasional drips, but it's far better than dealing with a jar of molasses. You can also keep it upside down when nearly empty, and not waste a single drop.
Foods such as barbecue sauce, ketchup, and mayonnaise are often sold in this type of flip-top dispenser. If you can't find molasses in such a bottle, or don't wish to buy that brand, you could re-use a washed out bottle from something else for your molasses. Or, you can buy them empty.
I buy it in gallon jugs (not all that frequently, but it's a better deal and does not go bad in my experience.) I find that to be far more convenient to pour neatly from than a jar. I usually touch the lip of the jug to the thing I'm pouring it into to get the vast majority of what would be drippage. And I actively avoid precisely measuring it, rather than have the waste and extra cleaning of a measuring cup coated with it. I glop some straight into the mixing bowl, usually.